Finite Group Databasebeta

← C139×#7205 #48001801

Subgroups — C139×#7205 #48001801

Order 35584.

372 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#1954×C139C211yesmaximal, characteristic
2C4×#99×C139C211yesmaximal, characteristic
3#1459×C139C211yesmaximal, characteristic
4C2×C4×D4×C139C2211yescharacteristic
5C2×C4⋊C8×C139C411yescharacteristic, complemented
6C2×#99×C139C412yes—
7C2×C22⋊C8×C139—21no—
8C2×C22⋊C8×C139—21no—
9C2×C22⋊C8×C139—21no—
10C2×C4×C8×C139C411yescharacteristic, complemented
11C4×C22⋊C4×C139—21no—
12#342×C139—21no—
13#324×C139C412yescomplemented
14#323×C139—21no—
15C22×D4×C139C2×C411yescharacteristic
16C23×C4×C139D411yescharacteristic
17C23×C4×C139D411yescharacteristic
18C22×C8×C139—21no—
19C22×C8×C139—21no—
20C22×C8×C139—41no—
21C4×D4×C139—41no—
22C4×D4×C139—41no—
23C2×C4⋊C4×C139C2×C411yescharacteristic
24C2×C22⋊C4×C139—22no—
25C2×C22⋊C4×C139D411yescharacteristic
26C2×C22⋊C4×C139Q811yescharacteristic
27C2×C42×C139—41no—
28C2×C42×C139C2×C411yescharacteristic
29C4⋊C8×C139—41no—
30#99×C139—22no—
31#99×C139C814yescomplemented
32C22⋊C8×C139—22no—
33C22⋊C8×C139—42no—
34C22⋊C8×C139—42no—
35C22⋊C8×C139—41no—
36C4×C8×C139—41no—
37#95×C139—41no—
38C24×C139C22⋊C411yescharacteristic
39C24×C139C4⋊C411yescharacteristic
40C2×D4×C139—41no—
41C2×D4×C139—41no—
42C2×D4×C139C2×C812yes—
43C2×D4×C139M1612yes—
44C22×C4×C139—21no—
45C22×C4×C139—21no—
46C22×C4×C139—21no—
47C22×C4×C139—21no—
48C22×C4×C139—41no—
49C22×C4×C139—41no—
50C22×C4×C139—41no—
51C22×C4×C139—41no—
52C22×C4×C139—42no—
53C22×C4×C139C4211yescharacteristic
54C22×C4×C139C22⋊C411yescharacteristic
55C22×C4×C139C22⋊C411yescharacteristic
56C22×C4×C139C4⋊C411yescharacteristic
57C22×C4×C139C4⋊C411yescharacteristic
58C2×C8×C139—22no—
59C2×C8×C139—41no—
60C2×C8×C139—41no—
61C2×C8×C139—42no—
62C2×C8×C139—41no—
63C2×C8×C139—41no—
64C2×C8×C139—41no—
65C2×C8×C139—81no—
66C2×C8×C139—81no—
67C4⋊C4×C139—41no—
68C22⋊C4×C139—24no—
69C22⋊C4×C139—41no—
70C22⋊C4×C139—41no—
71C22⋊C4×C139—42no—
72C42×C139—21no—
73C42×C139—21no—
74C42×C139—81no—
75C42×C139—81no—
76C23×C139—21no—
77C23×C139—21no—
78C23×C139—21no—
79C23×C139—21no—
80C23×C139—41no—
81C23×C139—41no—
82C23×C139—41no—
83C23×C139—41no—
84C23×C139#9511yescharacteristic
85C23×C139C22⋊C812yes—
86C23×C139C4⋊C812yes—
87D4×C139—42no—
88D4×C139—42no—
89C2×C4×C139—21no—
90C2×C4×C139—21no—
91C2×C4×C139—21no—
92C2×C4×C139—21no—
93C2×C4×C139—21no—
94C2×C4×C139—21no—
95C2×C4×C139—21no—
96C2×C4×C139—41no—
97C2×C4×C139—41no—
98C2×C4×C139—41no—
99C2×C4×C139—41no—
100C2×C4×C139—41no—
101C2×C4×C139—41no—
102C2×C4×C139—41no—
103C2×C4×C139—44no—
104C2×C4×C139—81no—
105C2×C4×C139—81no—
106C2×C4×C139—82no—
107C2×C4×C139—82no—
108C2×C4×C139C4×C811yescharacteristic
109C2×C4×C139#9711yescharacteristic
110C2×C4×C139#9911yescharacteristic
111C2×C4×C139#9911yescharacteristic
112C8×C139—42no—
113C8×C139—82no—
114C8×C139—81no—
115C22×C139—21no—
116C22×C139—21no—
117C22×C139—22no—
118C22×C139—22no—
119C22×C139—42no—
120C22×C139—42no—
121C22×C139—41no—
122C22×C139—41no—
123C22×C139—41no—
124C22×C139—41no—
125C22×C139—81no—
126C22×C139—81no—
127C22×C139#33611yescharacteristic
128C22×C139#34211yescharacteristic
129C22×C139#34411yescharacteristic
130C4×C139—21no—
131C4×C139—21no—
132C4×C139—21no—
133C4×C139—41no—
134C4×C139—41no—
135C4×C139—41no—
136C4×C139—84no—
137C4×C139#35311yescharacteristic
138C4×C139#35411yescharacteristic
139C2×C139—21no—
140C2×C139—21no—
141C2×C139—42no—
142C2×C139—42no—
143C2×C139#128211yescharacteristic
144C2×C139#139311yescharacteristic
145C2×C139#139511yescharacteristic
146#7205C13911yesmaximal, characteristic, direct product factor, Sylow
147C139#720511yescharacteristic, direct product factor, Sylow
148#1954C2×C13911yescharacteristic
149C4×#99C2×C13911yescharacteristic
150#1459C2×C13911yescharacteristic
151C2×C4×D4C22×C13911yescharacteristic
152C2×C4⋊C8C4×C13911yescharacteristic, complemented
153C2×#99C4×C13912yes—
154C2×C22⋊C8—21no—
155C2×C22⋊C8—21no—
156C2×C22⋊C8—21no—
157C2×C4×C8C4×C13911yescharacteristic, complemented
158C4×C22⋊C4—21no—
159#342—21no—
160#324C4×C13912yescomplemented
161#323—21no—
162C22×D4C2×C4×C13911yescharacteristic
163C23×C4D4×C13911yescharacteristic
164C23×C4D4×C13911yescharacteristic
165C22×C8—21no—
166C22×C8—21no—
167C22×C8—41no—
168C4×D4—41no—
169C4×D4—41no—
170C2×C4⋊C4C2×C4×C13911yescharacteristic
171C2×C22⋊C4—22no—
172C2×C22⋊C4D4×C13911yescharacteristic
173C2×C22⋊C4Q8×C13911yescharacteristic
174C2×C42—41no—
175C2×C42C2×C4×C13911yescharacteristic
176C4⋊C8—41no—
177#99—22no—
178#99C8×C13914yescomplemented
179C22⋊C8—22no—
180C22⋊C8—42no—
181C22⋊C8—42no—
182C22⋊C8—41no—
183C4×C8—41no—
184#95—41no—
185C24C22⋊C4×C13911yescharacteristic
186C24C4⋊C4×C13911yescharacteristic
187C2×D4—41no—
188C2×D4—41no—
189C2×D4C2×C8×C13912yes—
190C2×D4M16×C13912yes—
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—41no—
196C22×C4—41no—
197C22×C4—41no—
198C22×C4—41no—
199C22×C4—42no—
200C22×C4C42×C13911yescharacteristic
201C22×C4C22⋊C4×C13911yescharacteristic
202C22×C4C22⋊C4×C13911yescharacteristic
203C22×C4C4⋊C4×C13911yescharacteristic
204C22×C4C4⋊C4×C13911yescharacteristic
205C2×C8—22no—
206C2×C8—41no—
207C2×C8—41no—
208C2×C8—42no—
209C2×C8—41no—
210C2×C8—41no—
211C2×C8—41no—
212C2×C8—81no—
213C2×C8—81no—
214C4⋊C4—41no—
215C22⋊C4—24no—
216C22⋊C4—41no—
217C22⋊C4—41no—
218C22⋊C4—42no—
219C42—21no—
220C42—21no—
221C42—81no—
222C42—81no—
223C23—21no—
224C23—21no—
225C23—21no—
226C23—21no—
227C23—41no—
228C23—41no—
229C23—41no—
230C23—41no—
231C23#95×C13911yescharacteristic
232C23C22⋊C8×C13912yes—
233C23C4⋊C8×C13912yes—
234D4—42no—
235D4—42no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—44no—
251C2×C4—81no—
252C2×C4—81no—
253C2×C4—82no—
254C2×C4—82no—
255C2×C4C4×C8×C13911yescharacteristic
256C2×C4#97×C13911yescharacteristic
257C2×C4#99×C13911yescharacteristic
258C2×C4#99×C13911yescharacteristic
259C8—42no—
260C8—82no—
261C8—81no—
262C22—21no—
263C22—21no—
264C22—22no—
265C22—22no—
266C22—42no—
267C22—42no—
268C22—41no—
269C22—41no—
270C22—41no—
271C22—41no—
272C22—81no—
273C22—81no—
274C22#336×C13911yescharacteristic
275C22#342×C13911yescharacteristic
276C22#344×C13911yescharacteristic
277C4—21no—
278C4—21no—
279C4—21no—
280C4—41no—
281C4—41no—
282C4—41no—
283C4—84no—
284C4#353×C13911yescharacteristic
285C4#354×C13911yescharacteristic
286C2—21no—
287C2—21no—
288C2—42no—
289C2—42no—
290C2#1282×C13911yescharacteristic
291C2#1393×C13911yescharacteristic
292C2#1395×C13911yescharacteristic
subgroupG/H
centerC2×C4×C139#99
commutatorC2×C4C4×C8×C139
Frattini, cosocleC2×C4×D4C22×C139
socleC22×C139#342
prime radicalC22×D4×C139C2×C4
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C139 ◁ C22×C4×C139 ◁ C2×C4×D4×C139 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
5. C2×C4⋊C8×C139C4semidirect
10. C2×C4×C8×C139C4semidirect
13. #324×C139C4semidirect
31. #99×C139C8semidirect
146. #7205C139direct (N × H)
147. C139#7205direct (N × H)
152. C2×C4⋊C8C4×C139semidirect
157. C2×C4×C8C4×C139semidirect
160. #324C4×C139semidirect
178. #99C8×C139semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#1954×C1392
C4×#99×C1392
#1459×C1392
#7205139